Most studies analysing the infrastructure impact on regional growth show a positive relationship between both variables. However, the public capital elasticity estimated in a Cobb-Douglas function, which is the most common specification in these works, is sometimes too big to be credible, so that the results have been partially desestimated. In the present paper, we give some new advances on the real link between public capital and productivity for the Spanish regions in the period 1964-1991. Firstly, we find out that the association for both variables is smaller when controlling for regional effects, being industry the sector which reaps the most benefits from an increase in the infrastructural dotation. Secondly, concerning to the rigidity of the Cobb-Douglas function, it is surpassed by using the variable expansion method. The expanded functional form reveals both the absence of a direct effect of infrastructure and the fact that the link between infrastructure and growth depends on the level of the existing stock (threshold level) and the way infrastructure is articulated in its location relative to other factors. Finally, we analyse the importance of the spatial dimension in infrastructure impact, due to spillover effects. In this sense, the paper provides evidence of the existence of spatial autocorrelation processes that may invalidate previous results.